---Water vapor mixing ratio measurements
Water vapor mixing ratio measurements are performed by detecting two Raman signals (Ansmann et al., 1992; Whiteman et al., 1992). One of which is the return sig-nal from a reference atmospheric gas such as nitrogen and the other one is from the atmospheric gas of interest e.g. water vapor or any other gas with sufficient concen-tration. Typically, the Raman lidar technique uses the inelastic backscatter from ni-trogen and water vapor at 387 nm 407 nm, respectively (Whiteman, 2003). The ine-lastic signals from 607 nm and 660 nm are also an option. The ratio of the above re-turned signals, which can be expressed through Equation 3.2 after rearrangements, is proportional to the mixing ratio of water vapor, i.e. the ratio of the mass of water vapor to the mass of dry air in a given volume. Thus, water vapor mixing ratios de-rived from lidars require a calibration constant to adjust the signal ratio to meaning-ful values. The calibration constant can be determined in many ways where most commonly a reference system is used for calibrating the lidar water vapor mixing ratio (Foth et al., 2015; Navas-Guzmán et al., 2014). In Paper I, we evaluate the cali-bration factor from several different reference methods and appoint alternatives de-pending on the availability of these at the lidar location.
Measurements of water vapor mixing ratio in the atmosphere can be used to fur-ther derive RH (Mattis et al., 2002; Navas-Guzmán et al., 2014; Ristori et al., 2005).
The optical properties of the atmospheric particles strongly depend on RH values (Navas-Guzmán et al., 2019), therefore it can be used to track changes in the physical properties of the atmospheric particles (Haarig et al., 2017).
3.4 Retrieved aerosol properties
3.4.1 Optical properties
The determination of the particle extinction and backscatter coefficients using the lidar technique derives a handful of optical properties (Table 1). These optical prop-erties can be divided into two categories. Extensive optical propprop-erties which depend both on the nature (composition and shape) and the amount of the atmospheric aer-osol particles or clouds in the atmosphere, and intensive properties which depend only on the nature of the atmospheric component. The intensive properties can be used in multi-parametric relationships in the automatic aerosol and cloud classifica-tion (Kim et al., 2018; Müller et al., 2007; Nicolae et al., 2018).
Extensive properties
The backscatter and extinction coefficients are two extensive properties which have been already discussed. All lidars have a detection limit above which they can observe aerosol and cloud layers in the atmosphere. The detection limit is a function
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---of the nature and concentration ---of the scatterers. For example, the lidar instrument on board CALIPSO satellite has a detection limit of 2-4×10−4 km−1sr−1 backscatter in the troposphere (Powell et al., 2009; Winker et al., 2010). The undetected weak aero-sol and cloud layers in the atmosphere introduce underestimations of the aeroaero-sol and cloud burden in comparison studies of optical properties (Kacenelenbogen et al., 2014; Toth et al., 2018), as well as in calculations of radiative transfer (Thorsen et al., 2017).
Another extensive property is the Aerosol optical depth (AOD). The AOD is a meas-ure of the total aerosol extinction (Liou, 2002). The AOD is commonly used as an estimate of the amount of aerosol particles in the atmosphere, although it also de-pends on the optical properties of the aerosol. In the lidar technique, the parameter can be calculated by integrating the extinction coefficient profile from the surface up to the maximum possible measurement height range.
Intensive properties
An impressive effort has been made by the lidar community all around the world to define the intensive optical properties of pure aerosol types. Nicolae et al. (2018) summarize the up-to-date knowledge for the aerosol properties observed with elastic and Raman lidar systems. Cloud related optical properties have been reported by Weitkamp, (2005), Yorks et al., (2011), Voudouri et al., (2019) and references therein.
Explicitly, the intensive properties involve the following parameters:
Lidar ratio (LR) is the extinction to backscatter ratio. The molecular LR is range independent and well defined and can be therefore calculated. On the contrary, the particle LR can fluctuate with altitude as it depends on the size, shape, humidity, and chemical composition of the particles which is not constant throughout the atmos-pheric column. For example, dust particles at 532 nm wavelength have values be-tween 30-60 sr compared to marine aerosols whose range is bebe-tween 15 and 30 sr (Nicolae et al., 2018).
Ångström exponent (Å) describes the spectral dependence of the AOD (Ångström, 1929; Ansmann & Müller, 2005). It requires the performance of optical measurements of at least two wavelengths while additional wavelengths provide more detailed characterization of the observed atmospheric components (Baars, 2011). The Å is a rough measure of the size of the atmospheric components. Typical values range be-tween 0 to 3. Small particles correspond to large Å values and large particles to small Å values. For example, dust and marine particles show Å values lower than 1 indi-cating the presence of coarse mode particles in the atmosphere (Eck et al., 1999;
Schuster et al., 2006).
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---Linear particle depolarization ratio (δp) is a measure of sphericity of the atmospheric components. The degree of the depolarization is a function of the amount, size, re-fractive index and shape of the particles. The values generally range from 0 to 45%, so that irregularly shaped particles such as ice crystals, volcanic and desert dust in-troduce δp larger than 25% (Groß et al., 2011; Müller et al., 2007; Sassen, 2005). More-over, the shape of atmospheric particles, therefore the δp is affected by the hydration rate of the atmospheric particles (humid or dry), their lifetime (aged or fresh), as well as their physical composition (water or ice) (Ansmann et al., 2009; Granados-Muñoz et al., 2015). Beyond aerosol classification, δp is useful parameter in the re-trieval of microphysical aerosol properties.
Table 1. Optical properties derived with a lidar instrument.
Parameter Units
Extensive properties
Backscatter coefficient Mm-1 sr-1 Extinction coefficient Mm-1 Aerosol Optical Depth (AOD) - Water Vapor Mixing ratio
(WVMR) g kg-1
Intensive properties
Lidar ratio (LR) sr
Ångström exponent (Å) - Linear particle depolarization
ratio (δp) %
3.4.2 Microphysical properties
The transition from lidar derived aerosol particle optical properties to micro-physical properties is challenging due to the lack of adequate light-scattering models.
The lidar-derived optical properties obtained from a single scattering angle (180o) is too low to determine all the microphysical properties such as the effective radius, shape, refractive indices, single scattering albedo, size distribution and concentration of the particles. Therefore, inversion methods have been developed (Gasteiger et al., 2011; Müller et al., 1999; Osterloh et al., 2013; Veselovskii et al., 2002 & 2004). The mathematical inverse problem is ill-posed in which the desired microphysical prop-erty derives after several iterations and therefore different solutions instead of a unique one, introducing large uncertainties in the retrieved microphysical properties
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---(Papayannis et al., 2012; Pérez-Ramirez et al., 2013), thus regularization and con-straints are necessary. The basic input is a 3β + 2α (or 3 + 2) dataset, i.e. the three available backscatter coefficients at 1064, 532 and 355 nm and the two extinction co-efficients at 532 and 355 nm. This configuration works rather well in the case of spher-ical particles (e.g. Balis et al., 2010) but extensions have been developed to non-spher-ical particles for more accurate calculations (Müller et al., 2016; Veselovskii et al., 2010). A widely used light scattering model for non-spherical particles assumes that the particles are spheroids in shape (Dubovik et al., 2006). Veselovskii et al. (2010) implemented this model to lidar retrievals assuming aerosols to be a mixture of spheres and randomly oriented spheroids with a size-independent shape distribu-tion. However, the approach of spheroid like particles in lidar applications is rather restricted (Müller et al., 2010 & 2012). Tesche et al. (2019) demonstrated that in the case of non-spherical particles, additional information of linear particle depolarizat-ion measurements (3 + 2 + 1) improve the retrieved microphysical properties but the advantage of more depolarization channels (3 + 2 + X) is limited by the use of the non-ideal light scattering model which assumes non spherical particles to have spheroid like shape (Dubovik et al., 2006). Nonetheless, new light scattering models have been developed presenting more realistic particle geometries (Kahnert et al., 2016;
Nousiainen & Kandler, 2015). Synergistically, new light scattering models and novel lidar systems able to detect the atmospheric dust particle orientation (Tsekeri et al., 2019) could overwrite current lidar setups.
Cloud microphysical relevant parameters such as CCN and INP number concen-trations can be also estimated by means of lidar observations (Andreae, 2009; Ghan et al., 2006; Mamouri & Ansmann, 2017 & 2016 & 2015; Tan et al., 2019). To this end, these calculations are accompanied with large uncertainties linked to both lidar re-lated retrieval errors and errors introduced by the methodologies themselves (Ansmann et al., 2019; Tan et al., 2019). In fact, uncertainties to the retrieved CCN number concentration amounts to 50-200 % and regarding the INP number concen-trations up to a factor of 3 higher than CCN retrievals, has been determined (Ansmann et al., 2019). Predominately, the errors are linked to insufficient knowledge of the aerosol particle types and their corresponding physical properties, chemical properties, and coating effects due to aging in the atmosphere.
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---4 Main results
This chapter presents a synopsis of the main results and the relationship between Papers I to IV. For detailed results, kindly refer to the original publications included in the supplementary material.